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Durham University

Research & business

Research lectures, seminars and events

The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but  wish to enquire about attending one of the events please contact the organiser or host department.


 

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Events for 19 January 2021

Rainer Dietmann: Lines on cubic hypersurfaces

1:00pm, Zoom

Trevor Wooley has shown that every rational cubic hypersurface of dimension at least 35 contains a rational line. In this talk I want to report about recent joint work with Julia Brandes, reducing this 35 to 29 in the generic case of smooth cubic hypersurfaces. One of the key ingredients is a result by Browning, Heath-Brown and myself on intersections of cubic and quadric hypersurfaces. I also want to discuss the related problem of finding lines on cubic hypersurfaces defined over p-adic fields, to give explicit examples of smooth rational cubic hypersurfaces of dimension 9 not containing any rational line, and to mention a few applications of our results.

Contact herbert.gangl@durham.ac.uk, jack.g.shotton@durham.ac.uk for more information about this event.